One-to-One functions

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, meaning no two different inputs map to the same output.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function. If a vertical line intersects the graph at more than one point, the relation is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If any horizontal line intersects the graph more than once, the function is not one-to-one.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y coordinates in the ordered pairs and solve for y.

Front

What does it mean for a function to be not a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

Example of a one-to-one function: f(x) = 2x + 3. Is it one-to-one?

Back

Yes, because each input x produces a unique output.

Front

Example of a function that is not one-to-one: f(x) = x^2. Why is it not one-to-one?

Back

Because both positive and negative values of x produce the same output (e.g., f(2) = 4 and f(-2) = 4).

Front

What is the range of a one-to-one function?

Back

The range of a one-to-one function is the set of all possible outputs, where each output corresponds to exactly one input.

Front

If f(x) = 3x + 1, what is f(2)?

Back

f(2) = 3(2) + 1 = 7.

Front

If f(x) = x + 5, what is the inverse function?

Back

The inverse function is f^(-1)(x) = x - 5.